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(C) Given expression: $\sin A \cos A(	an A - \cot A)$Substitute $	an A = \frac{\sin A}{\cos A}$ and $\cot A = \frac{\cos A}{\sin A}$:$= \sin A \cos

Vedclass · Accepted Answer

$2\sin^{2} A - 1$

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(C) Given expression: $\sin A \cos A(	an A - \cot A)$Substitute $	an A = \frac{\sin A}{\cos A}$ and $\cot A = \frac{\cos A}{\sin A}$:$= \sin A \cos A \left( \frac{\sin A}{\cos A} - \frac{\cos A}{\sin A} ight)$Take the common denominator inside the bracket:$= \sin A \cos A \left( \frac{\sin^{2} A - \cos^{2} A}{\sin A \cos A} ight)$Cancel $\sin A \cos A$ from the numerator and denominator:$= \sin^{2} A - \cos^{2} A$Using the identity $\cos^{2} A = 1 - \sin^{2} A$:$= \sin^{2} A - (1 - \sin^{2} A)$$= \sin^{2} A - 1 + \sin^{2} A$$= 2\sin^{2} A - 1$

The simplified form of the given expression $\sin A \cos A(\tan A - \cot A)$ is (where $0^{\circ} \leq A \leq 90^{\circ}$)

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